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To find the new numerators, that is, how many 12ths each fraction is, we may take 2, 2, 3 and † of 12. Thus :

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and

8. Reduce,, and & to fractions having the least common denominator, and add them together.

9. Reduce

Ans.

1+2+2=44=11, amount. and to fractions of the least common de

nominator, and subtract one from the other.

Ans.

f, difference. 10. What is the least number that 3, 5, 8 and 10 will measure? Ans. 120. 11. There are 3 pieces of cloth, one containing 7 yards, another 13 yards, and the other 15 yards; how many yards in the 3 pieces.

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=

= 211. under the

Before adding, reduce the fractional parts to their least common denominator; this being done, we shall have, Adding together all the 24ths, viz. 18+ 20 21, we obtain 59, that is, We write down the fraction other fractions, and reserve the 2 integers to be carried to the amount of the other integers, making in the whole 371†, Ans. 12. There was a piece of cloth containing 343 yards, from which were taken 123 yards; how much was there

138 1320 157=1521

Ans. 37.

left?

348 34 12121

We cannot take 16 twenty-fourths (1) from 9 twenty-fourths, (;) we must, therefore, borrow 1 integer,= 24 twenty-fourths, (,) which, with, makes; we can now take from , and there will remain 17; but, as we borrowed, so also we must carry 1 to the 12, which makes it 13, and 13 from. 34 leaves 21. Ans. 21.

Ans. 21 yds.

13. What is the amount of of of a yard, of a yard, and of 2 yards?

Note. The compound fraction may be reduced to a simple fraction; thus, of; and of 2; then, + }+3=178=1% yds., Ans.

¶ 62. From the foregoing examples we derive the following RULE :-To add or subtract fractions, add or subtract their numerators, when they have a common denominator; otherwise, they must first be reduced to a common denomi nator.

Note. Compound fractions must Le reduced to simple fractions before adding or subtracting.

EXAMPLES FOR PRACTICE.

1. What is the amount of 4, 43 and 12? 2. A man bought a ticket, and sold of the ticket had he left?

3. Add together,,,, and . 4. What is the difference between 14

5. From 13 take .

6. From 3 take f.

7. From 147 take 48.

8. From of take of.

of

9. Add together 1124, 311%, and 1000g. 10. Add together 14, 11, 43,

and.

11. From take. From 3 take .

Ans. 17H

of it; what part Ans.

Amount, 238.

and 1673?

Ans. 118. Remainder, . Rem. 24.

12. What is the difference between 1 and †? and ? and ? and ? and ?

Rem. 988.

Rem. .

87

and ?

1-f?

13. How much is 1-? 1-? 1-q? 2-3 2-4? 21-47 34 1000-TO?

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REDUCTION OF FRACTIONS.

¶ 63. We have seen, ( 33,) that integers of one denomination may be reduced to integers of another denomination. It is evident, that fractions of one denomination, after the same manner, and by the same rules, may be reduced to fractions of another denomination; that is, fractions, like integers, may be brought into lower denominations by multiplication, and into higher denominations by division.

To reduce higher into LOWER To reduce lower into HIGHER

denominations.

(RULE. See ¶ 34.)

penny.

denominations.
(RULE. See T34.)

1. Reduce of a pound 2. Reduce of a penny to to pence, or the fraction of a the fraction of a pound. Note. Division is performNote. Let it be recollect- ed either by dividing the nu ed, that a fraction is multiplied merator, or by multiplying the either by dividing its denomi-denominator.

nator, or by multiplying its nu

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3. Reduce 12 of a pound to the fraction of a farthing. 1280 £. X 208, s. X

240

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4. Reduce of a farthing to the fraction of a pound. 29. ÷ 4 = d.÷ 12

12 d. X 4 = 1280=1828.÷20=3840-1290€.

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5. Reduce of a guinea to the fraction of a penny. 7. Reduce of a guinea to the fraction of a pound. Consult T 34, ex. 11.

20 s. in 1 £.

3840

Then, bo £. Ane.

=

6. Reduce of a penny to the fraction of a guinea.

8. Reduce of a pound to the fraction of a guinea.

10. Reduce

of a guinea

9. Reduce & of a moidore, at 36 s. to the fraction of a guinea. to the fraction of a moidore. 11. Reduce of a pound, 12. Reduce of an ounce Troy, to the fraction of an to the fraction of a pound

ounce.

Troy.

L*

13. Reduce of a pound, 14. Reduce

of an ounce

avoirdupois, to the fraction of to the fraction of a pound

an ounce.

15. A man has of a

avoirdupois.

16. A man has of a pint hogshead of wine; what part of wine; what part is that of

is that of a pint?
17. A cucumber grew to the
length of of a mile; what

part is that of a foot?

19. Reduce of of a

a hogshead?

18. A cucumber grew to the length of 1 foot 4 inches of a foot; what part

is that of a mile?

20. of a shilling is of

pound to the fraction of a shil-what fraction of a pound?

ling.

21. Reduce of of 3

pounds to the fraction of a what fraction of 3 pounds?

penny.

22. 180 of a penny is of

180 of a penny is

of what

part of 3 pounds?
penny is of

180 of a

of how many

pounds?

T 64. It will frequently be It will frequently be rerequired to find the value of a quired to reduce integers to fraction, that is, to reduce a the fraction of a greater defraction to integers of less de- nomination.

nominations.

1. What is the value of of a pound? In other words, Reduce of a pound to shillings and pence.

2. Reduce 13 s. 4 d. to the fraction of a pound.

13 s. 4 d. is 160 pence; there are 240 pence in a of a pound is 40133 shil-pound; therefore, 13 s. 4 d. is lings; it is evident from of 148 of a pound. That a shilling may be obtained is,-Reduce the given sum or some pence; of a shilling is quantity to the least denomina24d. That is,-Multiply tion mentioned in it, for a nu the numerator by that number merator; then reduce an inte which will reduce it to the next ger of that greater denominaless denomination, and divide tion (to a fraction of which it the product by the denominator; is required to reduce the givif there be a remainder, multiply en sum or quantity) to the and divide as before, and so on; same denomination, for a denomi the several quotients, placed one nator, and they will form the after another, in their order, fraction required.

will be the answer.

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Note. Let the pupil be required to reverse and prove the following examples:

21. What is the value of of a guinea?

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